The unbounded two-dimensional guiding-centre plasma

1995 ◽  
Vol 54 (1) ◽  
pp. 11-29 ◽  
Author(s):  
Michael K. -H. Kiessling
Keyword(s):  
Angular Momentum ◽  
Variational Principle ◽  
Mean Field ◽  
Analytical Techniques ◽  
Larmor Frequency ◽  
Two Dimensional ◽  
Algebraic Relation ◽  
Density Profiles ◽  
Translation Invariant ◽  
Computer Based

The thermal mean-field equilibrium of a translation-invariant, unbounded one- component guiding-centre plasma is studied by analytical techniques. A variational principle is constructed. It is shown that only radial symmetric, decreasing density profiles occur. Prescribing the total number of gyro centres N ∈ (0, ∞), the energy E ∈ (E0, ∞) and the canonical angular momentum M ∈ (0, ∞]) uniquely determines a profile. Metastable or unstable profiles do not exist. A simple algebraic relation between N, M, the guiding-centre temperature β−1 and the characteristic Larmor frequency ω is derived. This explains Williamson's computer-based observations.

scholarly journals Analysis of a Trapped Bose–Einstein Condensate in Terms of Position, Momentum, and Angular-Momentum Variance

Symmetry ◽  
2019 ◽  
Vol 11 (11) ◽  
pp. 1344 ◽  
Author(s):  
Ofir E. Alon
Keyword(s):  
Angular Momentum ◽  
Mean Field ◽  
Interaction Model ◽  
Einstein Condensate ◽  
Two Dimensional ◽  
Bose Einstein Condensate ◽  
Spatial Dimensions ◽  
The Many ◽  
Harmonic Interaction ◽  
Bose Einstein

We analyze, analytically and numerically, the position, momentum, and in particular the angular-momentum variance of a Bose–Einstein condensate (BEC) trapped in a two-dimensional anisotropic trap for static and dynamic scenarios. Explicitly, we study the ground state of the anisotropic harmonic-interaction model in two spatial dimensions analytically and the out-of-equilibrium dynamics of repulsive bosons in tilted two-dimensional annuli numerically accurately by using the multiconfigurational time-dependent Hartree for bosons method. The differences between the variances at the mean-field level, which are attributed to the shape of the BEC, and the variances at the many-body level, which incorporate depletion, are used to characterize position, momentum, and angular-momentum correlations in the BEC for finite systems and at the limit of an infinite number of particles where the bosons are 100 % condensed. Finally, we also explore inter-connections between the variances.

scholarly journals Effects of initial density profiles on massive star cluster formation in giant molecular clouds

2021 ◽  
Author(s):  
Yingtian Chen ◽  
Hui Li ◽  
Mark Vogelsberger
Keyword(s):  
Angular Momentum ◽  
Star Formation ◽  
Molecular Clouds ◽  
Globular Clusters ◽  
Cluster Formation ◽  
Initial Density ◽  
Giant Molecular Clouds ◽  
Density Profiles ◽  
Stellar Feedback ◽  
Gas Accretion

Abstract We perform a suite of hydrodynamic simulations to investigate how initial density profiles of giant molecular clouds (GMCs) affect their subsequent evolution. We find that the star formation duration and integrated star formation efficiency of the whole clouds are not sensitive to the choice of different profiles but are mainly controlled by the interplay between gravitational collapse and stellar feedback. Despite this similarity, GMCs with different profiles show dramatically different modes of star formation. For shallower profiles, GMCs first fragment into many self-gravitation cores and form sub-clusters that distributed throughout the entire clouds. These sub-clusters are later assembled ‘hierarchically’ to central clusters. In contrast, for steeper profiles, a massive cluster is quickly formed at the center of the cloud and then gradually grows its mass via gas accretion. Consequently, central clusters that emerged from clouds with shallower profiles are less massive and show less rotation than those with the steeper profiles. This is because 1) a significant fraction of mass and angular momentum in shallower profiles is stored in the orbital motion of the sub-clusters that are not able to merge into the central clusters 2) frequent hierarchical mergers in the shallower profiles lead to further losses of mass and angular momentum via violent relaxation and tidal disruption. Encouragingly, the degree of cluster rotations in steeper profiles is consistent with recent observations of young and intermediate-age clusters. We speculate that rotating globular clusters are likely formed via an ‘accretion’ mode from centrally-concentrated clouds in the early Universe.

SYMMETRY DECOUPLING IN LINEAR ALGEBRAIC VARIATIONAL SCATTERING PROBLEMS

1995 ◽  
Vol 06 (01) ◽  
pp. 105-121
Author(s):  
MEISHAN ZHAO
Keyword(s):  
Angular Momentum ◽  
Variational Principle ◽  
Total Angular Momentum ◽  
Numerical Calculations ◽  
Quantum Mechanical ◽  
Matrix Elements ◽  
Scattering Problems ◽  
Identical Particles ◽  
Generalized Newton

This paper discusses the symmetry decoupling in quantum mechanical algebraic variational scattering calculations by the generalized Newton variational principle. Symmetry decoupling for collisions involving identical particles is briefly discussed. Detailed discussion is given to decoupling from evaluation of matrix elements with nonzero total angular momentum. Example numerical calculations are presented for BrH2 and DH2 systems to illustrate accuracy and efficiency.

STUDY OF RANDOM PARTICLE TRAFFIC ON A MULTI-LATTICE JUNCTION

2013 ◽  
Vol 27 (09) ◽  
pp. 1350063 ◽  
Author(s):  
SHAODA LI ◽  
MINGZHE LIU ◽  
MIN ZHOU ◽  
YIZHANG YIN
Keyword(s):  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Low Density ◽  
Biological Transport ◽  
Traffic Dynamics ◽  
Exclusion Processes ◽  
Density Profiles ◽  
Random Particle ◽  
Asymmetric Exclusion Processes

In this paper, we investigate particle traffic on an m-input n-output (MINO) junction using totally asymmetric exclusion processes (TASEPs) under random sequential update. The model is suitable for description of biological transport. A general theoretical solution for traffic dynamics of TASEPs is developed based on a mean-field approximation. It is found that the low-density and high-density regions can be calculated qualitatively and quantitatively once the number of m and/or n is determined. The phase diagram, system current and density profiles are obtained through theoretical analysis and supported by Monte Carlo simulations. Comparison between a m-input n-output TASEP junction in random and parallel sequential updates has also been reported.

Implications of occupancy of 2s1/2 state in sd-shell within RMF+BCS approach

2017 ◽  
Vol 26 (11) ◽  
pp. 1750072 ◽  
Author(s):  
G. Saxena ◽  
M. Kumawat ◽  
M. Kaushik ◽  
U. K. Singh ◽  
S. K. Jain ◽  
...  
Keyword(s):  
Mean Field ◽  
The Other ◽  
Magic Numbers ◽  
Neutron Density ◽  
Shell Closure ◽  
Weakly Bound ◽  
Density Profiles ◽  
Relativistic Mean Field ◽  
Structure Formula ◽  
Bubble Structure

We employ the relativistic mean-field plus BCS (RMF+BCS) approach to study the behavior of [Formula: see text]-shell by investigating in detail the single particle energies, and proton and neutron density profiles along with the deformations and radii of even–even nuclei. Emergence of new shell closure, weakly bound structure and most recent phenomenon of bubble structure are reported in the [Formula: see text]-shell. [Formula: see text]C, [Formula: see text]O and [Formula: see text]S are found to have a weakly bound structure due to particle occupancy in 2[Formula: see text] state. On the other hand [Formula: see text]O, [Formula: see text]Ca and [Formula: see text]Si are found with depleted central density due to the unoccupied 2[Formula: see text] state and hence they are the potential candidates of bubble structure. [Formula: see text]C and [Formula: see text]O emerge as doubly magic with [Formula: see text] in accord with the recent experiments and [Formula: see text]S emerges as a new proton magic nucleus with [Formula: see text]. [Formula: see text] and [Formula: see text] are predicted as magic numbers in doubly magic [Formula: see text]O, [Formula: see text]Ca and [Formula: see text]Si, respectively. These results are found in agreement with the recent experiments and have consistent with the other parameters of RMF and other theories.

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